412 



NA TURE 



[August 22, 1901 



" In addition to the above, I remarked one of the extra 17 — 

 not a Perseid — which at 11.27 appeared at about the middle of 

 The Great Square and travelled right through the zenith, dis- 

 appearing near Corona and leaving behind it a remarkable 

 red shimmering trail which lasted for 4 or 5 seconds. 



"The above times given for the duration of trails were 

 obtained by counting seconds from judgment, not by a watch. 

 The observations were made whilst lying on my back, so that 

 nearly the whole of the sky above the available horizon 

 was observed." 



SAND WAVES IN TIDAL CURRENTS} 

 'T'HE sand waves dealt with in this paper are not the 

 ■'■ well-known " current mark," or ripple mark of 

 rivers, but the larger sort, first scientifically described 

 by Prof. Osborne Reynolds. These larger sand waves are 

 the normal production of a swift current when adequately 

 supplied with sand. The supposed condition of " uniform 

 drift" (the current picking up as much sand as it drops, 

 and therefore neither silting nor scouring) is really so 

 unstable that, when the current becomes sufficientjy swift 

 to hold sand in eddying suspension, it passes almost 

 suddenly into wave motion, uniform drift being replaced 

 by alternate silt and scour, giving ridges and furrows of 

 sand which travel down stream. The material of the 

 ridges is constantly being picked up by the current from 

 the weather slopes, and deposited upon the lee slopes. 

 Some explanation of the process was given in N.vrURE 

 (vol. Ixiii. p. 623, April 25) in the abstract of another 

 paper by the author:" this is further elaborated in the 

 paper now before us, which contains also details of the 

 observations and measurements carried out during the year 

 1900, which have not hitherto been published. 



The amplitude of the tidal sand waves is obviously limited 

 by the depth of water, and it follows that as the tide ebbs off 

 sand-banks, it tends to obliterate the ridges, leaving the banks 

 with the smoothed surface which is familiar. Sometimes pools 

 are left below the general level of the smoothed surface (Fig. i). 

 These have a steep and a gentle side, the former the lee slope 

 of one ridge, the latter the weather slope of the ne.\t ridge. 

 They are, in fact, homologous with the pits, called Fuljes, in 

 sandy deserts. 



and Aberdovey, North Wales, at Findhorn and Montrose, N.B., 

 and at the Dun Sands, on the Severn (Fig. 2), which are pro- 

 tected from the tide until well submerged by a rocky shoal, 

 which juts out from the left bank of the river. 



The observed wave-length or distance from ridge to ridge 

 varied from 3 feet 6 inches to 54 feet. The smallest of these 

 measurements was unusual. From 12 to 24 feet wave-lengths 

 were common. The steepest ridges had a wave-length 13 "39 



Where the conditions are such that the tide covers and leaves 

 the banks gently, though running strongly when the water is deep 

 upon them, the banks dry out with their wave surface almost 

 perfectly preserved. The required conditions were found by the 

 author in the tidal basins with narrow entrances at Barmouth 



1 Abstract of a paper by Dr. Vaughan Cornisti, read before the Royal 

 Geographical Society, June 10, and published m \\i<tGeogrnpht,-al Journal, 



" "On tlie Formation of Wave-surfaces in Sand," Scottish Geo- 

 graphical Magazine, vol. .wii., January 1901. 



NO. 1660, VOL. 64] 



Fig. 2. — Interpenetrating ridges on the Dun Sands, 



times as great as their height. In the model estuaries of Prof. 

 Osborne Reynolds the wavelength was twelve times the ampli- 

 tude. 



Fig. 3 shows the orderly march of the ridges upon a portion 

 of a sand-bank in the estuary of the Dovey, which the author 

 pegged out for purposes of measurement with stakes driven into 

 the sand to a depth of about 3 feet. There were five 

 transverse rows of stakes 15 feet from row to row, and in 

 each transverse row the distance from stake to stake was 20 feet. 

 This permitted the exact measurement of the position of 

 live wave-fronts along four sections. String stretched from 

 ^lake to stake at ihe two sides of the plot served as datum 

 lines and enabled amplitude and mean-sand-level to be 

 ;nken with tolerable accuracy along two sections. Mea- 

 urements were made once a day when the sands were 

 'hy. From June 2 to 5, 1900, the tides were diminishing 

 alter springs, and the average amplitude of the ridges dimi- 

 nished from 6"'34 to 3"7i with no perceptible change of 

 mean sand-level. The average wave-length in the same 

 line only diminished from 14' 3"'7 to 13' 6 "'6, and the 

 legularity of the wave-lengths improved, thus : — 



Percent, 

 of mean L. 

 On June I, av. diff. of successive Ls. = I3'4 

 ., 2 ,, „ =11-4 



„ 3 .. .. =107 



,, 4 ,. >■ = 4'4 



.. 5 „ „ = 6-6 



ijn June 5 the tidal current appeared to have fallen below 

 Mjnie critical velocity, and suddenly to have lost control of 

 ilie wave system. This is shown by the following table 

 (if the average advance of the ridges, which was : — 

 From June i to June 2 ... 3S"'o7 

 .. 2 „ „ 3 ••• 29"7S 

 „ ,, 3 .. .. 4 •■■ 3o"'57 

 „ 4 m .. 5 ■•• l"'4 



During neap tides the sands of the plot were almost smooth, 

 and such undulations as could be seen on the surface were 

 irregular and ill-defined. During the subsequent increase of 

 tides, however, the plot emerged one day all covered with 

 sharply defined ridges, which grew daily in height, and also (by 

 elimination of some of the ridges) in length. On June 15 the 

 average amplitude was 9"7i, with an average wave-length 

 of 11' 9". The increase of wave-length appears to take place 

 by the obliteration of certain ridges which find themselves un- 

 favourably placed owing to the too great growth of the ridge on 



